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EllipticF






Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticF[z,m] > Series representations > Generalized power series > Expansions at generic point m==m0 > For the function itself





http://functions.wolfram.com/08.05.06.0055.01









  


  










Input Form





EllipticF[z, m] \[Proportional] EllipticF[z, Subscript[m, 0]] + (1/4) ((2 EllipticE[z, Subscript[m, 0]])/(Subscript[m, 0] (1 - Subscript[m, 0])) - (2 EllipticF[z, Subscript[m, 0]])/ Subscript[m, 0] - Sin[2 z]/((1 - Subscript[m, 0]) Sqrt[1 - Subscript[m, 0] Sin[z]^2])) (m - Subscript[m, 0]) + (1/(16 (-1 + Subscript[m, 0])^2 Subscript[m, 0]^2 (1 - Sin[z]^2 Subscript[m, 0])^(3/2))) (2 (1 - Sin[z]^2 Subscript[m, 0])^(3/2) (2 EllipticE[z, Subscript[m, 0]] (-1 + 2 Subscript[m, 0]) + EllipticF[z, Subscript[m, 0]] (-1 + Subscript[m, 0]) (-2 + 3 Subscript[m, 0])) + Sin[2 z] Subscript[m, 0] (1 - (3 + 2 Sin[z]^2) Subscript[m, 0] + 4 Subscript[m, 0]^2 Sin[z]^2)) (m - Subscript[m, 0])^2 + O[(m - Subscript[m, 0])^3]










Standard Form





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MathML Form







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</apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 0 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <sin /> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> EllipticE </ci> <ci> z </ci> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 0 </cn> 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Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02





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